chapter2.page13

chapter2.page13 - t →∞ = a b . That is, as time goes on...

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3. LINEAR EQUATIONS AND BERNOULLI EQUATIONS 13 Solution From Example 3.3, x = e R adt ˆ R be R adt dt + C ! So x = e at ˆ R be at dt + C ! = e at ˆ b a e at + C ! , is the general solution. When C = 0 we have x = a b , a stead-state solution. Also, x = 0 is another steady-state solution, which can’t be represented in the general solution. We can rewrite x ( t ) as x ( t ) = a b + aCe - at , since lim t →∞ e - at = 0 So we have lim
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Unformatted text preview: t →∞ = a b . That is, as time goes on the population will gradually settles itself at the level of a b . The following picture shows that the solution curves approaches the line y = a b = 10 , with a = 0 . 2 and b = 0 . 002 . Figure 7. Population a = 0 . 2 and b = 0 . 02...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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